# Critical Tipping Angle Question

• Whenderson1
In summary, the conversation discusses finding the center of mass and tipping angle of a table, as well as determining the minimum force needed to tip the table. The center of mass is calculated using a torque calculation and found to be 0.78333 m from the edge of the table. The tipping angle is determined to be 32.6°. The conversation also mentions a question about the minimum force needed to lift one end of the table, but this remains unanswered.

#### Whenderson1

Okay so I've been reviewing previous tests for my midterm exam and I came across a question that I'm not too sure how to solve (I got this answer wrong and didn't bother to correct it so I don't know the solution) :(

The four legged table as shown has mass 30 kg. The table top has mass 20 kg and each leg is 2.5 kg. Find the centre of mass of the table and the angle at which the table will overturn. What minimum force applied to the upper edge of the table would put the table in a state of equilibrium and thus would tip with any larger force?

*note the table top has a width of 10 cm (couldn't draw it in)

|-----1.4 m-----|
_______________ _
| |
| |
| | 1.0 m
| | _
<---1.0 m--->

Okay so I think I figured out the first part. the center of mass of the table can be found by doing a torque calculation with the table rotated 90 degrees:
ƩTorque = 0
-Fgtabletop(d) + Fglegs(50-d) = 0
-196d + 4900 - 98d = 0
d = 16.666666
Therefore, Centre of mass = 95 cm - d = 95 - 16.66666 = 78.3333 cm = 0.78333 m
Now, the critical tipping angle can be calculated:
tan θ = (1/2width)/(centre of mass) = (0.5 m)/(0.783m)
θ = 32.6°

If someone could please verify my answer and help me with the last part regarding the minimum force applied to the upper edge it would be greatly appreciated. Thanks.

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ugh where did that ad come from.. ruined my picture :\

Assuming the legs of the table do not slide on the floor, what force do you need to apply so that one end of the table lifts up? If you keep pushing with this force does the table tip over, or can you still push with more force?

## 1. What is the critical tipping angle?

The critical tipping angle refers to the angle at which an object will start to tip over, given its shape, weight distribution, and the surface it is resting on. It is an important concept in physics and engineering, as it helps determine the stability of objects and structures.

## 2. How is the critical tipping angle calculated?

The critical tipping angle can be calculated using the formula: tan θ = μ, where θ is the critical angle and μ is the coefficient of friction between the object and the surface it is resting on. This formula takes into account the weight of the object, its shape, and the frictional force acting on it.

## 3. What factors affect the critical tipping angle?

The critical tipping angle can be affected by the weight and distribution of weight on the object, the shape and size of the object, the surface it is resting on, and the coefficient of friction between the object and the surface. Other factors such as wind or external forces can also play a role in the critical tipping angle.

## 4. Why is the critical tipping angle important?

Understanding the critical tipping angle is important for engineers and designers as it helps them determine the stability and safety of objects and structures. It can also be useful in everyday situations, such as loading a truck or arranging furniture, to prevent tipping and accidents.

## 5. Can the critical tipping angle be changed?

Yes, the critical tipping angle can be changed by altering the weight distribution of the object, changing the surface it is resting on, or by increasing or decreasing the coefficient of friction. In some cases, adding stabilizing elements such as supports or ballasts can also increase the critical tipping angle.